Asian Journal of Probability and Statistics

Normality is one of the essential assumptions in parametric statistical analysis practices that are regularly used in quantitative research. However, empirical research has tended to tackle the issue of normality as a matter of course in research procedure rather than a key aspect of research rigor. This article presents a holistic and integrative analysis of data normality in a manner that synthesises the foundations of theory, normality checks as methods of analysis, implications of a violation of normality in research analysis, and research solutions in different research studies. This research study exclusively relies on a desk research approach in a bid to compile findings on the topic of research from different methodological studies in statistics and research in economics, as well as research studies in social research.  This paper clearly presents a systematic discussion of how normality can be investigated for research data. In this respect, it covers the use of graphical techniques, formal statistical tests, and some computer-based procedures. It has also shown how different ways of diagnosing normality can be useful. It does not treat different methods as alternatives but, instead, points out their specific strengths and limits to help researchers understand when and for what reasons a specific method is more appropriate.  In addition, the researchers have discussed how the role of justification in larger samples using Central Limit Theorem is an essential topic, in focusing on the point that a larger sample size is effective in reducing, but certainly not obviating, a concern with normality. In this paper, it is also argued that a good approach to doing research in social science should strike a balance between analysing normality in each case, which it will informally contribute to a crucial methodological approach to doing research.